Questions: Chemical Kinetics

Question 1

For the reaction 2NO(g) + O₂(g) → 2NO₂(g), an experiment finds the rate law is rate = k[NO]²[O₂]. What can you conclude?

• A. The reaction proceeds in a single elementary step because the rate law matches the stoichiometry
• B. The reaction order was determined experimentally; the mechanism may involve multiple steps
• C. The rate constant k has units of M⁻¹s⁻¹ for this reaction
• D. The reaction is first order overall

Answer: (B)

Rate laws must be determined experimentally. Even when exponents match stoichiometric coefficients — as they happen to here — you cannot conclude the reaction is a single elementary step. The mechanism may be more complex, and this must be verified separately. Option C is also wrong: for this third-order reaction, k has units of M⁻²s⁻¹. Option D is wrong; the overall order is 2 + 1 = 3.

Question 2

For a first-order reaction, the half-life is the same regardless of the initial concentration of the reactant.

• T. True
• F. False

Answer: True

For a first-order reaction, t₁/₂ = ln(2)/k. Since k is a constant at a given temperature, the half-life is fixed — independent of [A]₀. This is a diagnostic: if the half-life remains constant as the reaction proceeds, the reaction is first-order. By contrast, for a second-order reaction t₁/₂ = 1/(k[A]₀), so successive half-lives get longer as the reactant is consumed.

Question 3

A reaction has a large negative ΔG (very thermodynamically favorable) but proceeds imperceptibly slowly at room temperature. How is this possible?

Model answer: ΔG determines thermodynamic spontaneity — whether the reaction is energetically downhill — but says nothing about the rate. Rate depends on the activation energy Ea, the energy barrier reactants must surmount to reach the transition state. A reaction can be thermodynamically favorable but kinetically blocked by a high activation energy barrier. Thermodynamics governs where a reaction goes; kinetics governs how fast it gets there.

Diamond converting to graphite is thermodynamically spontaneous but kinetically inert at room temperature because the activation energy is enormous. Catalysts lower Ea without changing ΔG — they accelerate the approach to equilibrium without changing where equilibrium lies. This separation between thermodynamic and kinetic control is one of the most important conceptual distinctions in chemistry.